I went to an exhibition of hats by the milliner Stephen Jones at the Victoria and Albert Museum today. The blurb in the exhibition catalogue implies that millinery is not a synonym of hat-making: "Distinct from hat-making, with its large-scale production of standard hat types, millinery focuses on the creation and decoration of elegant, experimental and often whimsical hats."
There were certainly plenty of elegant, experimental and whimsical hats in the exhibition, but dictionary definitions do regard millinery as a synonym of hat-making. Here's the OED definition: "The articles made or sold by milliners", and a milliner is "a person who designs, makes or sells women's hats".
The word milliner refers to the Italian city of Milan; it's an old word for a native or an inhabitant of that city. Milan was seemingly renowned for the fancy goods that were on sale there, and a milliner was originally, according to the OED, "a seller of fancy wares, accessories and articles of (female) apparel, esp. such as were originally made in Milan."